The computational worm: spatial orientation and its neuronal basis in C. elegans
Highlights
► C. elegans exhibits two forms of spatial orientation behavior, klinokinesis and klinotaxis, both of which require computation of the time derivative of chemosensory information. ► The time derivative is computed partly at the cellular and partly at the network level. ► The output of chemosensory neurons modulates the probability of stochastic course-correction events in klinokinesis ► It is hypothesized that course corrections in klinotaxis require phasic sensory gating at the level of motor neurons.
Introduction
Most animals are able to orient their locomotion with respect to a variety of cues in the environment (Figure 1). Typical cues include local gradients, landmarks, compass bearings related to the Earth's magnetic field or the position of celestial bodies such as the Sun, and internalized maps of the environment [1]. These abilities — collectively known as spatial orientation behaviors — are of scientific interest because they are fundamental to survival and goal directed. In addition, spatial orientation behaviors are unusually well suited to investigations of sensorimotor integration in the nervous system because the sensory cues that signal the goal, and the motor performance required to attain it, are directly observable and easily quantified.
Despite the interest and tractability of orientation behaviors, our understanding of their neuronal basis remains rudimentary. It is notable, therefore, that considerable progress has been made in understanding the neuronal mechanisms of spatial orientation in the nematode Caenorhabditis elegans. C. elegans exhibits a diverse repertoire of orientation behaviors in response to a variety of gradients by which it locates food, mating partners, and habitat. These behaviors include chemotaxis to salts and other soluble compounds [2, 3••], chemotaxis to odorants associated with food and mates [4••, 5], thermotaxis to preferred temperatures [5], aerotaxis to preferred levels of oxygen [6], and aerotaxis to low levels of carbon dioxide [7•]. In most of these behaviors, the gradient is sensed predominantly by one or more pairs of left–right symmetric neurons. These neurons contact the environment through a pair of sensory pores in the head. Although the right and left sensory pores are separated by 10 μm [8], the worm effectively samples the gradient at a single point in space. This is because the worm crawls on its right or left side which places the axis defined by the pores orthogonal to the plane of the substrate. The fact that the worm samples the environment at a single point entails that orientation behaviors are guided by either absolute stimulus strength or by the time derivative of sensory input as the animal moves through the environment. As discussed below, the physiology of C. elegans chemosensation supports the latter view.
C. elegans is an advantageous experimental system for the neuronal and theoretical analyses of behavior. The adult hermaphrodite has a compact nervous system of only 302 neurons, for which there exists an essentially complete anatomical reconstruction, the celebrated ‘wiring diagram’ of the worm [9••, 10•]. The genetic tractability of C. elegans together with recent technical advances in nematode neurophysiology — including patch clamp recording [11], calcium imaging [12], and optogenetics [13] — has accelerated the pace of research into the neuronal basis of behavior in this organism. C. elegans is also remarkably amenable to mathematical and computational modeling. The great majority of its neurons are morphologically simple, with just one or two processes which in most cases are unbranched [9••]. Neuronal processes are likely to be short relative to the predicted length constant of C. elegans neurons [11] suggesting that many C. elegans neurons are probably isopotential [11], or nearly so. Consequently, individual neurons can often be modeled as single electrical compartments. Consistent with their electrical compactness, and the absence of voltage gated sodium channels in the C. elegans genome [14], most C. elegans neurons probably do not fire classical, sodium-dependent action potentials [11, 15] and synaptic transmission between C. elegans neurons is likely to be graded [16]. Thus, the widely used formalism of real-time recurrent neural networks [17•], which is formally equivalent to networks of single compartment neurons with graded synaptic input–output functions, is a better approximation of network-level function in C. elegans than in most other systems.
Two main behavioral strategies have been identified for spatial orientation behaviors in C. elegans. These are klinokinesis and klinotaxis, also known, respectively, as the pirouette [18, 19••, 20] and weathervane mechanisms in C. elegans [21••]. Both strategies were first identified in gradients of tastants such as inorganic salts and other soluble compounds [2]. As discussed below, essential neuronal elements of both strategies have been delineated.
Section snippets
Klinokinesis behavior
The klinokinesis strategy involves a biased random walk up the gradient (Figure 2a). In the laboratory, C. elegans orientation behaviors are mainly studied in the aqueous environment of the surface of a moist agar filled plate. Locomotory thrust is generated by snake-like undulations. These undulations occur in the dorso-ventral plane because worms crawl on their sides. In a uniform concentration of a chemoattractant, locomotion in C. elegans consists of periods of relatively straightforward
Neuronal mechanisms of klinokinesis
A candidate neural circuit for klinokinesis in gradients of tastants has been identified (Figure 2c). Although earlier modeling studies provided existence proofs for circuits of C. elegans-like neurons sufficient to compute dC(t)/dt at the network level [30, 31], subsequent neurophysiological experiments demonstrated that this quantity is actually computed jointly at the cellular and network levels [32••, 33]; for a possible exception to this rule, see Ref. [34]. Three left–right pairs of
Klinotaxis behavior
In the klinotaxis strategy, by definition, the animal's course is continuously corrected toward the line of steepest ascent up the gradient (Figure 3a). Klinotaxis is therefore a deterministic rather than a stochastic strategy. C. elegans steers by adjusting the angle of its head with respect to the rest of body [48, 49]. Course corrections in klinotaxis take place during the side-to-side movements of the worm's head that occur as part of normal undulatory locomotion in nematodes. Klinotaxis
Neuronal mechanisms of klinotaxis
Neuronal ablations together with anatomical reconstructions imply the circuit shown in Figure 3c. The ASE neurons provide almost all of the chemosensory input to the klinotaxis circuit [21••]. The off-cell, ASE-right, is the dominant member of the ASE class in that ablating it produces a strong deficit in klinotaxis, whereas ablation of the on-cell, ASE-left, has little or no effect unless combined with ablation of its sister cell [21••]. However, when both ASE neurons are ablated, the
Symmetry breaking in klinotaxis
A model of symmetry breaking in C. elegans klinotaxis based on the principle of phasic sensory gating [52, 53] has been proposed [50•]. The model is based on two main assumptions. First, it assumes that undulations of the neck are produced by antiphasic synaptic inputs to dorsal and ventral neck muscle motor neurons (Figure 3c). Such inputs might originate from a central pattern generator, for example. Second, the model assumes a nonlinear relationship between motor neuron synaptic input and
Evolution of on–off coding
Why is on–off coding pervasive in C. elegans sensory neurons required for spatial orientation behavior? In the early visual system of vertebrates and insects, where on–off coding is well known [55, 56], it has been suggested that this coding scheme reflects a requirement for energy efficiency [57]. The alternative strategy, in which single neurons encode increases and decreases in the stimulus, requires high basal rates of activity to achieve a similar dynamic range. On–off coding can also be
Phylogenetic considerations
Spatial orientation has been investigated in a wide range of aquatic organisms in addition to C. elegans. These include prokaryotes, unicellular organisms, insect larvae, crustaceans, and fish. Despite this diversity in species, only two main types of sampling strategies have been identified: single-point sampling as described above for C. elegans, and stereo sampling in which the organism simultaneously makes use of a widely separated pair chemosensory structures. Comparison of orientation
Outlook
Spatial orientation behaviors in C. elegans are well suited to investigations of sensory processing and sensorimotor integration. The neuronal analysis of klinokinesis has yielded a simple circuit motif for computing the time derivative of sensory information that can be applied to other sensory modalities. Theoretical analysis of klinotaxis has provided a model of how representations of behavior are integrated with biological outcomes to generate adaptive responses. These findings lead to
References and recommended reading
Papers of particular interest, published within the period of review, have been highlighted as:
• of special interest
•• of outstanding interest
Acknowledgements
The author was supported during this research by grant R01-MH051383 from the National Institute of Mental Health. C. Derby provided useful discussion. S. Faumont, E. Heckscher, T. Lindsay, and K. McCormick provided critical comments on the manuscript.
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